978-1-4244-7467-7/10/$26.00 ©2010 IEEE

2010 IREP Symposium- Bulk Power System Dynamics and Control – VIII (IREP), August 1-6, 2010, Buzios, RJ, Brazil

Influence of Inverter-Based Distributed Generator Interface Control on the

Performance of Power Distribution Systems

Daniel Petean José Carlos M. Vieira Ricardo Q. Machado

Federal Institute of Education, Science and Technology of São

Paulo dpetean@cefetsp.br

Department of Electrical Engineering São Carlos School of Engineering

University of São Paulo - USP jcarlos@sc.usp.br

Department of Electrical Engineering São Carlos School of Engineering

University of São Paulo - USP rquadros@sc.usp.br

Abstract This paper presents a comparative analysis about the influences of three inverter-based distributed generators control modes on several important aspects of distribution networks. The control modes investigated are constant current, constant reactive and active power, and constant voltage and active power. The investigated aspects are steady-state voltage profile, network losses, short-circuit currents and voltage sags. The results are very useful to guide utility engineers to define operating requirements for this type of distributed generator, aiming at minimizing possible negative impacts to the distribution grid. Introduction Distributed generation (DG) has gained widespread attention recently due to market deregulation, technological advances, governmental incentives, and environment impact concerns [1]-[3]. However, the real benefits that DG can provide to distribution systems depend on the type of generator, its size, control strategies and penetration level. Therefore, it is highly recommended to perform a detailed study before installing DG in the distribution network, so that engineers can determine how it affects the grid operation. For example, in [4] there is an extensive investigation about the impacts of distributed synchronous and induction machines on the performance of the distribution system, such as steady-state voltage profile, active power losses, short-circuit level and voltage stability. The results showed that the type of the machine as well as its control mode can significantly influence those characteristics, in both positive and negative manner. Although synchronous and induction distributed generators directly connected to the grid are widely employed in DG applications, there has been an increased interest in inverter-based distributed generators. This has occurred mainly due to their control flexibility, as well as to the augmented interest in using renewable energy

resources. Inverter-based DG includes photovoltaic arrays, fuel cells, microturbines, some types of wind turbines and energy storage devices [3]. Despite of this variety of technologies, their impacts on distribution networks have not been extensively investigated so far, similar to what was done in [4]. Researches on this subject are focused on islanding detection and islanded operation [5]-[7]. In order to fill this gap, this work analyses the influences of different inverter-based DG interface control strategies on the performance of a typical distribution network. The control strategies analyzed are constant current (I control), constant active and reactive power (PQ control) and constant active power and voltage (PV control). Although such control strategies are covered in technical literature with focus in other aspects, there is no consensus on what is the best control mode under the distribution network perspective. Thus, it is important to understand the impacts caused by this choice on several technical factors. In this context, this work aims at outlining the advantages and disadvantages of each control strategy on steady-state voltage profile and regulation, electrical power losses, voltage stability, short-circuit level and voltage sags. The results can be a useful technical guide for utility engineers and energy producers to decide which control strategy is more suitable, taking into account the main characteristics of distribution network. Network Component Models The basic structure of inverter-based distributed generators employed in this work is depicted in Fig. 1. According to this figure, three-phase voltage and currents (VA, VB, VC and IA, IB, IC) measured at the point of common coupling (PCC) are processed by the interface control, which generates the control signals to the pulse width modulation (PWM) signal generator. This device generates the pulses or switch signals to control de inverter. There is a DC voltage source connected to the inverter. Such voltage source represents the primary energy source (fuel cell, PV cell etc) connected to a DC/DC or AC/DC converter, which is connected to a

capacitor. This simplification is valid because usually the capacitor has high energy storage capacity [3], [8] and because it is assumed that the output of the DC sources is regulated and fixed in the time frame between 0 and 1 second [9]. Besides, in the analyses carried out in this work, transient simulations last less than 1 second, consequently, based on the above-mentioned statements, the results obtained here are valid. Furthermore, in Fig. 1 the distributed generator is connected to a filter with inductance LF and capacitance CF. In addition, distributed generators are connected to the grid through step-up transformers. This is not represented in Fig. 1, but it is considered in the test system used in the simulations. Finally, the “Control” block in the figure will be detailed in the next sections and it depends on the adopted control strategy: I control, PQ control and PV control.

Fig. 1 Basic structure of an inverter-based distributed generator. The three-phase voltage and currents measured at the PCC are converted to dq0 quantities inside the “Control” block through eq. (1):

( ) ( )( ) ( )

⋅

+−−−−

+−

=

C

B

A

V

V

V

sensensen

v

vq

vd

21

21

21

32

32

32cos3

2coscos

3

2

0

πθπθθ

πθπθθ (1)

Equation (1) is also applied to currents. In (1), the angle θ is the inverter terminal voltage angle, which is calculated by a phase locked loop (PLL). The PLL operation is depicted Fig. 2. In this figure, kpPLL and kiPLL are the proportional and integral gains, respectively, and ωo is the rated angular frequency. PLL also calculates the electrical frequency of the inverter terminal voltage.

Fig. 2 Three-phase PLL model.

Finally, the control output ud and uq are converted into three-phase abc voltages, which are used in a PWM signal generator to generate the switching pulses. The following subsections present block diagrams of the three control strategies employed in this paper. Constant Current Control (I Control)

In this case, the distributed generator interface is configured to supply constant current by controlling the values of d-axis and q-axis currents, id and iq, to be equal to reference values idref and iqref, respectively. Moreover, decoupled components (idωPLLLF and iqωPLLLF) are introduced as described in [10]. This control strategy is depicted in the block diagram of Fig. 3. In this figure, kpi and kii are the proportional and integral gains, respectively.

Fig. 3 Block diagram of constant current controller.

Constant Active and Reactive Power Control (PQ

Control)

Under this control strategy, the inverter is configured to supply constant active and reactive power, by controlling id and iq to produce active and reactive power equal to Pref e Qref, respectively. To achieve such a goal, there are two control loops, as depicted in Fig. 4: a power control loop and a current control one, which has the same characteristics of the block diagram shown in Fig. 3. The power control loop generates the current references to the

V A, VB , VC

IA, IB , IC

VDC

LF

CF

Distributed Generator

PWM

u d, uq

pulses

Filter

CONTROL

+ +

ωPLL

abc

s

kk iPLL

pPLL +

vq

ωff

VA

dq

VB

VC

sin, cos

θPLL

sin θPLL , cos θPLL

∫

s

kk ii

pi +

s

kk ii

pi ++ iqref

idref

iq

-

id

uq

+

-

ud

+ +

-

+ +

+

vd

vq

IqωPLLLF

IdωPLLLF

current control loop. In the figure, kpp and kip are the proportional and integral gains of the power controller. kpi and kii were defined previously. The active and reactive powers are calculated by equations (2) and (3), respectively.

qqdd ivivP ⋅+⋅= (pu) (2)

dqqd ivivQ ⋅−⋅= (pu) (3)

Fig. 4 Block diagram of constant active and reactive power controller.

Constant Power and Voltage Control (PV Control)

The inverter is controlled to supply constant active power keeping its terminal voltage also constant. The block diagram is depicted in Fig. 5, and it is derived from the control blocks presented in [5] and [7]. Notice that the structure is very similar to the one shown in Fig. 4, but the reactive power quantities were replaced by the measured and reference terminal voltage, V and Vref, respectively. The voltage control loop has a droop characteristic, which allows slightly variations of terminal voltage in order to avoid the controller oscillatory behavior. Typically, the droop gain is 5%.

Fig. 5 Block diagram of constant active power and terminal voltage controller.

Distribution Network The distribution system analyzed in this work is presented in Fig. 6. This network comprises a 132 kV subtransmission system represented by a Thévenin equivalent circuit with three-phase short-circuit power equal to 150 MVA. The DG Group comprises ten 300 kVA inverted-based distributed generators. Each one is connected to the grid through a 13.8/0.69 kV step-up transformer. It is assumed that all of generators are identical and that the control strategies are uniformly applied to all inverters. The loads are modeled as constant impedance types. The transformers, loads and distributed generators as well as the controllers’ parameters are shown in the Appendix.

132 kV 150 MVA

132/13.8 kV

Sub

1 2

3 4

Line 1 Line 2 ∆ Yn

5 6 7

Line 3 Line 4 Line 5

L1 900 kW 360 kvar

DG Group

L2 650 kW 240 kvar

L3 520 kW 210 kvar

L4 450 kW 180 kvar

L5 36 0 kW 140 kvar

L6 350 kW 140 kvar

Fig. 6 Single line diagram of the distribution network.

Steady-State Voltage Profile and Active

Power Losses Voltage violations due to the presence of distributed generators can considerably limit the amount of power supplied by these generators in distribution networks [3]. Before installing (or allowing the installation of) distributed generators, utility engineers must analyze the worst operating scenarios to guarantee that the network voltages will not be adversely affected by the generators. These scenarios are characterized by the following [4]:

• Maximum generation and maximum demand; • Maximum generation and minimum demand.

In this paper, it was considered that the minimum demand corresponds to 20% of the maximum demand. Moreover, the steady-state voltage limits were adopted as 0.93 pu and 1.05 pu. The setpoint values of the DG interface controllers are the following:

• I control: Idref = 0.30 pu; Iqref = 0; • PQ control: Pref = 300 kW; Qref = 0 kvar; • PV control: Pref = 300 kW; Vref = 1 pu.

Results are shown in Fig. 7(a) and Fig. 7(b) for maximum and minimum loading conditions, respectively. In both

s

kk

ippp +

Pref

P

+

-

Qref

Q

+

-

s

kk ii

pi +

s

kk ii

pi +

+ iqref

idref

iq

-

id

uq

+

-

ud

+ +

-

+ +

+

vd

vq

IqωPLLLF

IdωPLLLF

s

kk

ippp +

Power Control Loop Current Control Loop

s

kk

ip

pp +

Pref

P

+

-

Vref

V

+

-

s

kk ii

pi +

s

kk ii

pi +

+ iqref

idref

iq

-

id

uq

+

-

ud

+ +

-

+ +

+

vd

vq

IqωPLLLF

IdωPLLLF

s

kk iv

pv +

droop

+

figures, the performances of I control and PQ control modes are very similar, so that their corresponding curves are superimposed.

(a) Maximum loading

(b) Minimum loading

Fig. 7 Steady-state voltage profile.

From Fig. 7(a) it is clearly observed that the presence of DG at maximum loading condition improves significantly the voltage profile. In this particular case, PV control caused a slight improvement in the voltage profile in comparison with the other control strategies. Under minimum loading condition (Fig. 7(b)), the PV control also presented an advantage, since it contributed to keep the nodal voltages near 1 pu. Thus, this control type can be used to improve the voltage regulation of the grid. Notice that in the case of I and PQ controls and minimum loading, the nodal voltages tend to increase at the buses near the DG Group, which may violate steady-state voltage magnitude limits if more generators are added to the system.

Steady-State Voltage Variation Due to Generator

Disconnection

One important issue regarding the DG integration to distribution networks is the voltage variation that can occur after the DG disconnection. It is desired that such variation be as small as possible in order to not cause power quality problems, since the actuation of voltage regulators and on-load tap changers transformers is slow [3]. Therefore, to estimate this variation, an index VI1 proposed in [4] is calculated through (1):

= 1

∑ −

∑

× 100 (1)

where nb is total number of buses,

is the magnitude of the nodal voltage of bus i in the presence of distributed generators, and is the , magnitude of the nodal voltage of bus i without distributed generators. The results are summarized in Table 1, considering that the DG Group is tripped off during maximum and minimum loading. It can be observed that the value of VI1 is small for all control strategies. Therefore, in this case, the influence of the DG Group disconnection is not a major concern. The index associated with PV Control is slightly larger than the others because of the reactive power injected by the DG Group. Operating under I Control and PQ Control, the DG Group does not inject or absorb reactive power, as can be concluded form the control setpoints presented previously. The more the reactive power injected into the system by the DG, the higher the index VI1.

Table 1 Steady-state voltage variation due to DG disconnection.

(%) DG Control Minimum loading Maximum loading

I Control 0.15 0.23 PQ Control 0.15 0.23 PV Control 0.16 0.28

Steady-State Voltage Regulation

Other important issue related to steady-state voltage is the regulation characteristic of the network, which means how much the nodal voltage change between maximum and minimum loading cases. It is desirable that the nodal voltage change as little as possible during load variation. In order to evaluate such characteristic the following global index is employed [4]:

= 1 −

× 100 (2)

2 3 4 5 6 70.93

0.95

0.97

0.99

1

1.01

1.02

1.04

1.05

Bus

Vo

lta

ge

(p

u)

Without DG

I Control

PQ Control

PV Control

2 3 4 5 6 70.93

0.95

0.97

0.99

1

1.01

1.02

1.04

1.05

Bus

Vo

lta

ge

(p

u)

Without DG

I Control

PQ Control

PV Control

where is the magnitude of the nodal voltage of bus i during maximum loading, and is the magnitude of bus i during minimum loading condition. The results are shown in Table 2, where it can be observed that the DG Group operating under PV Control leads to the best characteristic, i. e. the reactive power injected by the generators changes according to the load variation, providing a good voltage regulation. This does not occur for the other control strategies; however their results are better than the ones obtained without DG.

Table 2 Voltage regulation.

DG Control (%)

I Control 2.74 PQ Control 2.73 PV Control 0.60 Without DG 3.20

Active Power Losses

Although the active power losses do not pose as a barrier to the penetration of DG, it is an important economic factor. Therefore, in this section the impact of the operating control modes of the DG Group on the power losses is analyzed. The results are show in Fig. 8.

(a) Maximum loading.

(b) Minimum loading.

Fig. 8 Active power losses.

In Fig. 8, it can be seen that, in this particular case, the presence of DG reduces the total losses in the case of maximum loading (Fig. 8(a)) for any interface control strategy. The opposite situation can be observed in the case of minimum loading (Fig. 8(b)), where the total losses are increased substantially in the presence of DG. This behavior is due to high current values flowing through lines 1, 2 and 3 after the DG installation. In this situation, electrical power losses at minimum loading may restrain the amount of power supplied by the DG Group. Voltage Stability In general, it is expected that the installation of generators near load centers leads to an increase in the system voltage stability margin. However, the impact on this margin is strongly dependent on the amount of active power injected into the system and on the amount of reactive power exchanged between the generator and the distribution system. Therefore, in order to assess the impacts of the three DG interface control modes on the voltage stability margin, the PV curves of the system are obtained [4] through increasing gradually the active and reactive power loads, beginning at the point of maximum loading (3230 kW and 1270 kvar) and keeping the DG Group supplying constant active power according to the setpoint values. The results are shown in Fig. 9, where the case without DG is also shown for comparison purposes. Bus 7 was chosen because its nodal voltage is the smallest among the other buses.

Fig. 9 PV curves of bus 7. Important conclusions can be drawn from Fig. 9. At first, it can be seen that the generators operating under PQ control lead to the largest voltage stability margin, whereas PV control leads to the smallest. Nevertheless, the generators operating under PV control help the network voltage support, because the amount of reactive power injected into the electrical system increases, as the

1

10

100

1000

10000

100000

Line 1 Line 2 Line 3 Line 4 Line 5 Total

Act

ive

Po

we

r Lo

sse

s (W

)

Without DG

I Control

PQ Control

PV Control

1

10

100

1000

10000

100000

Line 1 Line 2 Line 3 Line 4 Line 5 Total

Act

ive

Po

we

r Lo

sse

s (W

)

Without DG

I Control

PQ Control

PV Control

300300300300 400400400400 500500500500 600600600600 700700700700 800800800800 900900900900 1000100010001000 1100110011001100 1200120012001200 1300130013001300 1400140014001400 15001500150015000.30.30.30.3

0.40.40.40.4

0.50.50.50.5

0.60.60.60.6

0.70.70.70.7

0.80.80.80.8

0.90.90.90.9

1111

Active Power of Bus 7 (kW)Active Power of Bus 7 (kW)Active Power of Bus 7 (kW)Active Power of Bus 7 (kW)

Vo

lta

ge

of

Bu

s 7

(p

u)

Vo

lta

ge

of

Bu

s 7

(p

u)

Vo

lta

ge

of

Bu

s 7

(p

u)

Vo

lta

ge

of

Bu

s 7

(p

u)

Without DGWithout DGWithout DGWithout DG

I ControlI ControlI ControlI Control

PQ ControlPQ ControlPQ ControlPQ Control

PV ControlPV ControlPV ControlPV Control

loading increases. Figure 10 shows this fact in detail. Notice that under PV control mode, the system can be subjected to a higher loading without violating the lower steady-state voltage limit (0.93 pu). In this situation the load of bus 7 can be increased until 1100 W, whereas under I and PQ control modes, it can be increased until 660 W. Generators operating under PV control mode lead to the smallest voltage stability margin because the controller loses stability as the system loading is augmented. This occurs due to the reactive power injected by the DG Group into the system, which increases as the load is augmented. This can be observed in Fig. 11, where the reactive power of one DG is shown. The same behavior is observed for the other generators of the DG Group. The DG reactive power increases in an attempt to regulate nodal voltage, consequently the DG loading increases, violating its rated capacity. The result is that the controller is no longer capable to generate the desired voltage at the DG terminals, and the voltage collapses as observed. In this situation, the distributed generator would be tripped off, but this was not considered in this simulation. The behavior observed for PV control does not occur in the case of PQ and I control because their reactive power outputs are fixed.

Fig. 10 PV curves of bus 7 in detail.

Fig. 11 DG reactive power - PV control. Short-Circuit Currents The installation of distributed generators can increase significantly the short-circuit level of the distribution system. Therefore, overcurrent protection device settings as well as the equipments withstand capabilities against short-circuit currents must be assessed after the DG placement. In this context, the impacts of inverter-based DG on the short-circuit level is analyzed in this section, considering the three control modes. A solid three-phase-to-ground short-circuit is applied at bus 6 at t = 1 second and cleared in 3 cycles. All the ten generators of the DG Group were in operation during the disturbance. Figure 12(a) shows the short-circuit current contribution of the DG Group for each control type. It can be seen that the PV control is responsible for the highest fault current contribution, whereas under I control the DG Group fault contribution can be neglected. The total fault current of this worst case is shown in Fig. 12(b), where it is compared with the case without DG. In this situation, the fault current with DG is about 20% higher than the total fault current without DGs. Therefore, the number of inverter-based distributed generators operating under PV control may pose as a disadvantage of such control mode if the network short-circuit level is close to the equipments short-circuit withstand capabilities. The same conclusion is valid to the PQ control mode.

300300300300 400400400400 500500500500 600600600600 700700700700 800800800800 900900900900 1000100010001000 1100110011001100 12001200120012000.900.900.900.90

0.910.910.910.91

0.950.950.950.95

0.930.930.930.93

0.940.940.940.94

0.950.950.950.95

0.960.960.960.96

0.970.970.970.97

0.980.980.980.98

0.990.990.990.99

1.001.001.001.00

Active Power of Bus 7 (kW)Active Power of Bus 7 (kW)Active Power of Bus 7 (kW)Active Power of Bus 7 (kW)

Vo

lta

ge

of

Bu

s 7

(p

u)

Vo

lta

ge

of

Bu

s 7

(p

u)

Vo

lta

ge

of

Bu

s 7

(p

u)

Vo

lta

ge

of

Bu

s 7

(p

u)

Without DGWithout DGWithout DGWithout DG

I ControlI ControlI ControlI Control

PQ ControlPQ ControlPQ ControlPQ Control

PV ControlPV ControlPV ControlPV Control

300300300300 400400400400 500500500500 600600600600 700700700700 800800800800 900900900900 1000100010001000 11001100110011000000

50505050

100100100100

150150150150

200200200200

250250250250

300300300300

350350350350

Active Power of Bus 7Active Power of Bus 7Active Power of Bus 7Active Power of Bus 7

DG

Re

ac

tive

Po

we

r (k

va

r)D

G R

ea

cti

ve

Po

we

r (k

va

r)D

G R

ea

cti

ve

Po

we

r (k

va

r)D

G R

ea

cti

ve

Po

we

r (k

va

r)

(a) DG group short-circuit current

(b) Total short-circuit current

Fig. 12 Fault currents for a three-phase-to-ground short-circuit at bus 6.

Voltage Sags During short-circuits, voltage sags occur in the system buses, and the presence of distributed generators may influence their magnitude and duration [4]. Thus, this section presents an analysis about voltage sags due to balanced three-phase faults applied to bus 6 of the electrical system shown in Fig. 6. The fault was cleared within 3 cycles. Figure 13 presents the dynamic response of the nodal voltage at bus 2, considering the DG control modes and the case without DG for comparison. It can be seen the positive influence of the DG Group operating under PV control mode, because both the voltage drop and its recovery time are smaller than the other cases. This occurs because of the reactive power injection of the DG Group operating under PV control. The other control modes did not influenced the voltage sag magnitude and duration. The same behavior was observed in the other buses, so that it is not necessary to show all the voltages.

Fig. 13 RMS voltage at bus 2 for a three-phase-to-ground short-circuit at bus 6. Conclusions

This paper presented a comparative analysis concerning the influence of three inverter-based DG control modes on various operating characteristics of a typical power distribution system. The analysis showed that despite of the positive influence of the PV control mode on the steady-state voltage profile and voltage sags, it can limit the penetration of DG in a distribution network with high short-circuit level. This is an important concern if the inverter protection is not fast enough to trip the generator before its fault contribution reaches the highest value. In addition, PV control contributed to a poor voltage stability margin, however it also led to the highest network loading without violating the low steady-state voltage limit. Thus, for the distribution system operation, granting voltage support at high loading conditions may be more important than having a large voltage stability margin. Finally, although the results presented in this paper can help utility engineers to assess the impacts of inverter-based DG connection, further aspects should be investigated. One of major importance is the inverter controller design and evaluation when the DG is operating under a severe loading and its influence on distribution network power quality. These topics need further development and they are under investigation.

Acknowledgments

The authors would like to thank Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for the financial support (Project number 2008/03184-7).

0.95 1 1.05 1.1 1.15-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1200

Time (s)

Cu

rre

nts

(A

)

I Control

PQ Control

PV Control

0.95 1 1.05 1.1-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Time (s)

Cu

rre

nts

(A

)

Without DG

PV Control2196 A2196 A2196 A2196 A

1817 A1817 A1817 A1817 A

0.95 1 1.05 1.10.85

0.9

0.95

1

1.05

Time (s)

Vo

lta

ge

of

Bu

s 2

(p

u)

Without DG

I Control

PQ Control

PV Control

0.88 pu

0.86 pu

Appendix The data of distribution network presented of Fig. 6 is presented in this appendix. Table 3 shows the line parameters.

Table 3 Line data.

Line Resistance (ΩΩΩΩ) Reactance (ΩΩΩΩ)

Line 1 0.5624 2.5318 Line 2 0.5000 2.2505 Line 3 0.6248 1.4066 Line 4 0.5000 1.1252 Line 5 0.3750 0.8439

The substation transformer parameters are given in Table 4.

Table 4 Substation transformer data.

Parameter Value

Rated power (MVA) 50 Primary voltage (kV) 132

Secondary voltage (kV) 13.8 Transformer impedance (%) 10 Magnetizing impedance (%) neglected Primary winding connection ∆

Secondary winding connection Y grounded Each inverter-based distributed generator has rated power equal to 300 kVA, and 690 V as nominal voltage. The controllers’ parameters are given in Table 5.

Table 5 Inverter-based generator data.

Parameters I Control PV Control PQ Control

VDC (V) 2000 2000 2000 PWM carrier

frequency (Hz)

8000 8000 8000

kii 500 100 500 kpi 0.5 0.5 0.5 kip --- 500 100 kpp --- 0.5 0.5 kpv --- 0.5 --- kiv --- 500 ---

droop --- 0.05 --- LF (mH) 2 2 2 CF (µF) 35.18 12,60 19.79 KpPLL 50 50 50 KiPLL 500 500 500

Table 6 shows the DG step-up transformer data and Table 7 the parameters of the subtransmission network Thévenin equivalent circuit.

Table 6 DG step-up transformer data.

Parameter Value

Rated power (MVA) 1 Primary voltage (kV) 13.8

Secondary voltage (kV) 0.69 Transformer impedance (%) 4 Magnetizing impedance (%) neglected Primary winding connection ∆

Secondary winding connection Y

Table 7 Thévenin equivalent circuit data.

Parameter Value

Three-phase short-circuit power (MVA)

150

Rated voltage (kV) 132 Resistance (Ω) 0 Indutctance (H) 0.308

References [1] CIGRÉ Working Group 37.23, “Impact of increasing contribution

of dispersed generation on the power system,” CIGRÉ, Technical Report, 1999.

[2] CIRED Working Group 4, “Dispersed Generation,” CIRED, Technical Report, 1999.

[3] N. Jenkins, R. Allan, P. Crossley, D. Kirschen, and G. Strbac, Embedded Generation, 1st ed. Institute of Electrical Engineers, 2000.

[4] W. Freitas, J. C. M. Vieira, A. Morelato, L. C. P. da Silva, V. F. da Costa, and F. A. B. Lemos, “Comparative analysis between synchronous and induction machines for distributed generation applications,” IEEE Trans. Power Delivery, vol. 21, no. 1, pp. 301-311, Feb. 2006.

[5] H. H. Zeineldin, E. F. El-Saadany, and M. M. A. Salama, “Impact of DG Interface Control on Islanding Detection and Nondetection Zone,” IEEE Trans. Power Delivery, vol. 21, no. 3, pp. 1515-1523, Jul. 2006.

[6] X. Wang, “Investigation of positive feedback anti-islanding scheme for inverter-based distributed generation,” Ph.D., thesis, Dept. of Electrical and Computer Engineering, University of Alberta, 2008.

[7] Z. Jiang, and X. Yu, “Active power-voltage control scheme for islanding operation of inverter-interfaced microgrids”, in Proc.

2009 IEEE Power Engineering Society General Meeting., p. 7. [8] S. Buso, and P. Mattavelli, Digital Control in Power Electronics,

Morgan & Claypool Publishers, 2006, p. 158. [9] N. Nimpitiwan, G. T. Heydt, R. Ayyanar, S. Suryanarayann, “Fault

current contribution from synchronous machine and inverter based distributied generators,” IEEE Trans. Power Delivery, vol. 22, no. 1, pp. 634-641, Jan. 2007.

[10] M. Prodanovic, and T. C. Green, “Control of power quality in inverter-based distributed generation,” in Proc.28th Annual

Conference of the IEEE Industrial Electronics Society, 2002, pp. 1185-1189.